On Mixing Measures for Axiom A Diffeomorphisms

Let f be a diffeomorphism satisfying Smale’s Axiom A and X an infinite basic set such that $f|X$ is topologically mixing. Let M denote the space of f-invariant measures on X with the weak topology. It is shown that for a dense set of measures μ in M, the system (X,f,μ ) is Bernoulli. It follows that “in general” the elements of M are weakly mixing.